ECONOMICS 100A: MICROECONOMICS

Transcription

1 ECONOMICS 100A: MICROECONOMICS Summer Session II 2011 Tues, Thur 8:00-10:50am Center Hall 214 Professor Mark Machina Office: Econ Bldg 217 Office Hrs: Tu/Th 11:30-1:30 TA: Michael Futch Office: Sequoyah Hall 228 Office Hours: Fri 1-3 Discussion Section: Friday 10:00-11:50am Center Hall 214 DATE TOPIC TEXT / MATH HANDOUT Aug. 2 Introduction & Mathematical Review #1 Ch. 1 / Sects. A, B Aug. 2 Mathematical Review #1 (continued) 2 / C Aug. 4 Consumer Preferences: Utility Functions and Indifference Curves 3.1 Aug. 4 Consumer Preferences: Utility Functions and Indifference Curves (continued) 3.2 Aug. 9 Mathematical Review #2 D, E Aug. 9 Utility Maximization and Demand Functions 3.3, 3.4 Aug. 11 Utility Maximization and Demand Functions (continued) 4.1 Aug. 11 Consumer Surplus and Welfare Analysis Aug. 16 Mathematical Review #3 F,G,H Aug. 16 Mathematical Review #3 (continued) F,G,H Aug. 18 (Thursday) Midterm Exam Aug. 23 Comparative Statics of Demand 4.2 Aug. 23 Comparative Statics of Demand (continued) 4.3 Aug. 25 Comparative Statics of Demand (continued) 4.4, 4.5 Aug. 25 Supply of Labor: The Labor-Leisure Decision 5.5 Aug. 30 Supply of Capital: The Consumption-Saving Decision 15.4 Aug. 30 Supply of Capital: The Consumption-Saving Decision (continued) 15.4 Sep. 1 Decision Making under Risk and Uncertainty 16.1, 16.2 Sep. 1 Decision Making under Risk and Uncertainty (continued) 16.3, 16.4 Sep. 3 (Saturday) FINAL EXAM 8:00-11:00am TBA TEXT & READINGS: Microeconomics: Theory and Applications with Calculus by Jeffrey Perloff (Custom UCSD Edition). There is also a Soft Reserve Package which contains the Math Handout, practice problems, and old exam questions. You are responsible for all the material in the assigned portions of the text and the Math Handout. EXAMS: Grades are determined on the basis of a Midterm Exam and a Final Exam. COURSE WEB PAGE: The course web page is at: This page contains useful information and materials about the course, including the Math Handout, Old Exam Questions, and information about the exams.

2 ECON 100A COURSE OUTLINE I. INTRODUCTION AND MATHEMATICAL REVIEW #1 a. Domain of Microeconomic Analysis b. Circular Flow Diagram c. Stocks vs. Flows and the Dimensions of Economic Variables d. Calculus Review (Math Handout, Section A) Derivatives, Partial Derivatives and the Chain Rule Approximation Formulas for Small Changes in Functions (Total Differentials) e. Elasticity (Math Handout, Section B) Absolute, Proportionate and Percentage Changes in Variables Definition of Elasticity and Examples Constant Elasticity Functions f. Level Curves of Functions (Math Handout, Section C) Definition and Graphical Illustration Algebraic Formula for a Level Curve Formula for the Slope of a Level Curve II. CONSUMER PREFERENCES: UTILITY FUNCTIONS & INDIFFERENCE CURVES a. Commodities, Commodity Bundles and Preferences Commodities are Typically Flows, not Stocks Issue of Divisibility Weak Preference, Strict Preference and Indifference Relations b. Utility Functions Preferences are defined over Commodity Bundles, not Individual Commodities Utility Functions and Total Utility Curves Important Examples: Linear, Cobb-Douglas, Leontief Marginal Utility and Marginal Utility Curves Hypothesis of Diminishing Marginal Utility Monotonic Transformations of Utility Functions c. Indifference Curves and the Marginal Rate of Substitution Deriving a Consumer s Indifference Curves from Their Utility Function General Properties of Indifference Curves: One Through Every Commodity Bundle Downward Sloping and Can t Cross Marginal Rate of Substitution (MRS) Graphical Interpretation: Slope of the Indifference Curve Algebraic Formula: Ratio of Marginal Utilities Hypothesis of Diminishing Marginal Rate of Substitution III. MATHEMATICAL REVIEW #2 a. Scale Properties of Functions (Math Handout, Section D) b. Solving Optimization s (Math Handout, Section E) General Structure of Optimization s First and Second Order Conditions for Unconstrained Optimization s First Order Conditions for Constrained Optimization s c. Corner Solutions and Inequality Constraints

3 IV. UTILITY MAXIMIZATION AND DEMAND FUNCTIONS a. Utility Maximization Subject to a Budget Constraint Graphical Illustration First Order Conditions for Utility Maximization Two Interpretations of the First Order Conditions Second Order Conditions (Hypothesis of Diminishing MRS) Corner Solutions: Graphical Illustration and Algebraic Condition Indirect Utility Functions and their Properties b. Regular ( Marshallian ) Demand Curves and Demand Functions Definition of Regular Demand Functions Examples: Cobb-Douglas, Leontief, Linear General Properties of Demand Functions: Walras Law Scale Invariant in Prices and Income Relationship between Price Elasticities & Income Elasticity for a Good Market Demand Functions c. Consumer Surplus and Welfare Analysis Consumer Surplus Equivalent and Compensating Variation Expenditure Functions V. MATHEMATICAL REVIEW #3 a. Comparative Statics of Solution Functions (Math Handout, Section F) b. Comparative Statics of Equilibria (Math Handout, Section G) c. Comparative Statics of Optimal Value Functions (Math Handout, Section H) VI. COMPARATIVE STATICS OF DEMAND a. Income Changes Income-Consumption Locus Engel Curves: Definition and Graphical Derivation Income Elasticity Superior, Normal and Inferior Goods Income Elasticity and Budget Shares Relationship Between Income Elasticities of All Goods Algebraic Derivation of the Effect of an Income Change b. Price Changes Price-Consumption Locus Graphical Derivation of Marshallian Demand Curves Own Price Elasticity Price Elasticity and Expenditures Cross Price Elasticity Gross Substitutes and Gross Complements Algebraic Derivation of the Effect of a Price Change c. Compensated Price Changes and Compensated ( Hicksian ) Demand Functions Graphical Illustration of a Compensated Price Change Graphical Derivation of Compensated Demand Curves Algebraic Derivation of Compensated Demand Functions Algebraic Derivation of the Effect of a Compensated Price Change

4 d. The Slutsky Equation Expressing Each of the Three Basic Changes in Terms of the Other Two Graphical Illustration Algebraic Formulation and Informal Proof Giffen Goods VII. SUPPLY OF LABOR: THE LABOR-LEISURE DECISION Income-Leisure Space and the Labor-Leisure Decision First Order Conditions for Optimal Supply of Labor Comparative Statics: Income and Substitution Effects Backward Bending Supply of Labor Curves Kinked Budget Lines and the Overtime Decision VIII. SUPPLY OF CAPITAL: THE CONSUMPTION-SAVINGS DECISION Intertemporal Income and Consumption Streams Interest Rates and Discounted Present Value of a Stream Intertemporal Utility Maximization First Order Conditions and Interpretation Comparative Statics: Income and Substitution Effects IX. DECISION MAKING UNDER RISK AND UNCERTAINTY a. Outcomes, Lotteries and Expected Value Choice over Lotteries Expected Value The St. Petersburg Paradox b. Expected Utility Two-Stage Lotteries and the Independence Axiom von Neumann-Morgenstern Utility Functions and Expected Utility c. Risk Aversion Properties of Risk Averse Preferences Arrow-Pratt Measure of Risk Aversion Risk Aversion and Wealth d. Measures of Risk Aversion e. Demand for Insurance f. Investment in a Risky Asset

5 FAMOUS OPTIMIZATION PROBLEMS IN ECONOMICS Optimization Objective Function Constraint Control Variables Parameters Solution Functions Optimal Value Function Consumer s U(x 1,...,x n ) utility p 1 x p n x n = I x 1,..., x n commodity p 1,..., p n, I prices and income x i (p 1,...,p n,i) regular demand s V(p 1,...,p n,i) Expenditure Minimization p 1 x p n x n expenditure level U(x 1,..., x n ) = u desired utility level x 1,..., x n commodity p 1,..., p n, u prices and utility level h i (p 1,...,p n, u ) compensated demand s e(p 1,...,p n, u ) expenditure Labor/Leisure Decision U(H,I ) utility I = I 0 + w (168 H) H, I leisure time, disposable inc. w, I 0 wage rate and nonwage income 168 H(w, I 0 ) labor supply V(w, I 0 ) Consumption/ Savings Decision U(c 1,c 2 ) utility c 2 = I 2 + (1+i) (I 1 c 1 ) c 1, c 2 consumption I 1, I 2, i income stream and interest rate c 1 (I 1, I 2, i), c 2 (I 1, I 2, i) consumption s V(I 1, I 2, i) Long Run Cost Minimization w L + r K total cost F(L,K) = Q desired output L, K factor Q, w, r desired output and L(Q,w,r), K(Q,w,r) output-constrained factor demand s LTC(Q,w,r) long run total cost Long Run Profit Maximization (in terms of Q) P Q LTC(Q,w,r) total profit none Q output level P, w, r output price and Q(P,w,r) long run supply (P,w,r) long run profit Long Run Profit Maximization (in terms of L and K) P F(L,K) w L r K total profit none L, K factor P, w, r output price and L(P,w,r), K(P,w,r) factor demand s (P,w,r) long run profit